DM-GAA

ISSN 1509-9415 (print version)

ISSN 2084-0373 (electronic version)

https://doi.org/10.7151/dmgaa

Discussiones Mathematicae - General Algebra and Applications

Cite Score (2023): 0.6

SJR (2023): 0.214

SNIP (2023): 0.604

Index Copernicus (2022): 121.02

H-Index: 5

Discussiones Mathematicae - General Algebra and Applications

Article in volume

Authors:

Y.T. Oyebo

Yakub Tunde Oyebo

Department of Mathematics
Lagos State University Ojo
Lagos State, 102101 Nigeria

email: oyeboyt@yahoo.com

B. Osoba

Benard Osoba

Bell University of Technology, Ota

email: benardomth@gmail.com

0000-0003-0840-8046

T.G. Jaiyeola

Temitópe Gbólahan Jaiyeola

Department of Mathematics
Obafemi Awolowo University
Ile Ife 220005, Nigeria

email: jaiyeolatemitope@yahoo.com

Title:

Crypto-automorphism group of some quasigroups

PDF

Source:

Discussiones Mathematicae - General Algebra and Applications 44(1) (2024) 57-72

Received: 2022-01-18 , Revised: 2022-09-20 , Accepted: 2022-09-20 , Available online: 2023-04-17 , https://doi.org/10.7151/dmgaa.1433

Abstract:

In quasigroup and loop theory, a pseudo-automorphism (with single companion) is known to generalize automorphism. In this work, the set of crypto-automorphisms (with twin companion) of a quasigroup with right and left identity elements were shown to form a group. For a quasigroup with right and left identity elements, some results on autotopic characterizations of crypto-automorphisms were established and used to deduce some subgroups of the crypto-automorphism group of a middle Bol loop. The crypto-automorphism group and Bryant-Schneider group (this has been used in the study of the isotopy-isomorphy of some varieties of loops e.g. Bol loops, Moufang loops, Osborn loops) of a loop were found to coincide.

Keywords:

quasigroup, loop, crypto-automorphism, Bryant-Schneider group

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